Proposition 99.12.3 (0D1C)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 99: Quot and Hilbert Spaces
Section 99.12: Relative morphisms
Proposition 99.12.3 (cite)

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Proposition 99.12.3. Let $S$ be a scheme. Let $Z \to B$ and $X \to B$ be morphisms of algebraic spaces over $S$ . Assume $X \to B$ is of finite presentation and separated and $Z \to B$ is of finite presentation, flat, and proper. Then $\mathit{Mor}_ B(Z, X)$ is an algebraic space locally of finite presentation over $B$ .

Proof. Immediate consequence of Lemma 99.12.2 and Proposition 99.9.4. $\square$

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